Finite Group DatabasebetaFinite Group Databasebeta| order | 27468 |
| automorphism | ? |
| homology | Abelianization (H1) = C22×C9 · Schur multiplier (H2) = C2 |
| direct product | C2×#28351526 |
| derived, Hall | C7×C109 ⋊ C22×C9 |
| Hall | #20293536 ⋊ C22 |
| Hall | C2×D7×C109 ⋊ C9 |
| Sylow | C109 ⋊ C2×D7⋊C9 |
| Hall | C2×D7 ⋊ #11758279 |
| Sylow | C7 ⋊ C22×#11758279 |
60 conjugacy classes of subgroups.
| transitive degree | μt(G) = 13734 |
1122 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(27468, 43);